cp's OEIS Frontend

A266985 Least positive integer x such that n + x^3 = y^2 + z^5 for some positive integers y and z, or 0 if no such x exists.

%I A266985 #6 Jan 08 2016 04:02:02
%S A266985 7,1,2,34,1,55,3,5,30,1,3,242,6,7,3,26,1,4,2,7,5,3,62,3,77,1,107,10,2,
%T A266985 2,3,6,1,2,128,1,1,4,3,11,1,3,2,6,7,5,22,1,50,1,7,5,6,16,3,3,1,2,4,62,
%U A266985 2,17,19,6,1,8,14,1,4,3,11
%N A266985 Least positive integer x such that n + x^3 = y^2 + z^5 for some positive integers y and z, or 0 if no such x exists.
%C A266985 The general conjecture in A266277 implies that for any integer m there are positive integers x, y and z with m + x^3 = y^2 + z^5.
%C A266985 See also A266277 and A266528 for similar conjectures.
%H A266985 Zhi-Wei Sun, <a href="/A266985/b266985.txt">Table of n, a(n) for n = 0..3800</a>
%e A266985 a(0) = 7 since 0 + 7^3 = 10^2 + 3^5.
%e A266985 a(3) = 34 since 3 + 34^3 = 150^2 + 7^5.
%e A266985 a(8) = 30 since 8 + 30^3 = 101^2 + 7^5.
%e A266985 a(11) = 242 since 11 + 242^3 = 3420^2 + 19^5.
%e A266985 a(766) = 90891 since 766 + 90891^3 = 11850281^2 + 906^5.
%t A266985 SQ[n_]:=SQ[n]=IntegerQ[Sqrt[n]]
%t A266985 Do[x=1;Label[bb];Do[If[SQ[n+x^3-y^5],Print[n," ",x];Goto[aa]],{y,1,(n+x^3-1)^(1/5)}];x=x+1;Goto[bb];Label[aa];Continue,{n,0,70}]
%Y A266985 Cf. A000290, A000578, A000584, A266152, A266153, A266230, A266231, A266314, A266363, A266364, A266528, A266548.
%K A266985 nonn
%O A266985 0,1
%A A266985 _Zhi-Wei Sun_, Jan 08 2016